Question

for questions 1 through 3, find the mean, median, mode, and range for each set of data. 1. 10, 71, 83, 91, 38, 55, 74, 5, 59, 91 2. 769, 818, 826, 786, 751, 803, 769, 759, 201

Explanation:

Step1: Organize the data (Question 1)

First, we sort the data set: \(5, 10, 38, 55, 59, 71, 74, 83, 97, 97\)

Step2: Calculate the Mean (Question 1)

The mean is the sum of all values divided by the number of values.
Sum \(= 5 + 10 + 38 + 55 + 59 + 71 + 74 + 83 + 97 + 97 = 599\)
Number of values \(n = 10\)
Mean \(= \frac{599}{10} = 59.9\)

Step3: Calculate the Median (Question 1)

Since \(n = 10\) (even), the median is the average of the 5th and 6th values.
5th value \(= 59\), 6th value \(= 71\)
Median \(= \frac{59 + 71}{2} = 65\)

Step4: Determine the Mode (Question 1)

The mode is the value that appears most frequently. Here, \(97\) appears twice, others once. So mode \(= 97\)

Step5: Calculate the Range (Question 1)

Range is the difference between the maximum and minimum values.
Max \(= 97\), Min \(= 5\)
Range \(= 97 - 5 = 92\)

Step6: Organize the data (Question 2)

Sort the data set: \(201, 751, 759, 769, 769, 786, 803, 818, 826\)

Step7: Calculate the Mean (Question 2)

Sum \(= 201 + 751 + 759 + 769 + 769 + 786 + 803 + 818 + 826 = 6582\)
Number of values \(n = 9\)
Mean \(= \frac{6582}{9} = 731.33\) (rounded to two decimal places)

Step8: Calculate the Median (Question 2)

Since \(n = 9\) (odd), the median is the 5th value.
5th value \(= 769\)
Median \(= 769\)

Step9: Determine the Mode (Question 2)

The mode is the value that appears most frequently. Here, \(769\) appears twice, others once. So mode \(= 769\)

Step10: Calculate the Range (Question 2)

Range is the difference between the maximum and minimum values.
Max \(= 826\), Min \(= 201\)
Range \(= 826 - 201 = 625\)

Answer:

Question 1:

• Mean: \(59.9\)
• Median: \(65\)
• Mode: \(97\)
• Range: \(92\)

Question 2:

• Mean: \(731.33\)
• Median: \(769\)
• Mode: \(769\)
• Range: \(625\)